Course Description and Outline

This course is a continuation of Calculus I. After a review of limits, derivatives, and integrals, we will develop various integration techniques (integration by parts, trig substitution, etc.) and then go on to apply them in various situations, such as finding areas, volumes, and lengths of curves. We will also study some applications of integration to physics, engineering, economics, etc. The second half of the course will be devoted to the study of infinite sequences and series. The main question for this part is whether an infinite sum adds up to something, and the ultimate goal will be to come up with an infinite series representation for a given function. What time is left will be devoted to the study of parametric equations and polar coordinates. A section-by-section outline of the course is given below.

The more general objective of this course is to continue providing you with a deeper understanding and working knowledge of calculus, while in the process strengthening your analytical skills, increasing your ability to communicate mathematics symbolically and orally, making you comfortable with reading and understanding mathematics on your own, and developing an appreciation for calculus as one of the greatest intellectual developments in history.

Here is a more detailed outline of the course. All sections refer to Calculus: Concepts and Contexts, 4th edition, by James Stewart.